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<div class="header">
  <div class="summary">
<a href="classEigen_1_1PartialPivLU-members.html">List of all members</a> &#124;
<a href="#pub-methods">Public Member Functions</a>  </div>
  <div class="headertitle">
<div class="title">Eigen::PartialPivLU&lt; MatrixType_ &gt; Class Template Reference<div class="ingroups"><a class="el" href="group__DenseLinearSolvers__chapter.html">Dense linear problems and decompositions</a> &raquo; <a class="el" href="group__DenseLinearSolvers__Reference.html">Reference</a> &raquo; <a class="el" href="group__LU__Module.html">LU module</a></div></div>  </div>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template&lt;typename MatrixType_&gt;<br />
class Eigen::PartialPivLU&lt; MatrixType_ &gt;</h3>

<p>LU decomposition of a matrix with partial pivoting, and related features. </p>
<dl class="tparams"><dt>Template Parameters</dt><dd>
  <table class="tparams">
    <tr><td class="paramname">MatrixType_</td><td>the type of the matrix of which we are computing the LU decomposition</td></tr>
  </table>
  </dd>
</dl>
<p>This class represents a LU decomposition of a <b>square</b> <b>invertible</b> matrix, with partial pivoting: the matrix A is decomposed as A = PLU where L is unit-lower-triangular, U is upper-triangular, and P is a permutation matrix.</p>
<p>Typically, partial pivoting LU decomposition is only considered numerically stable for square invertible matrices. Thus LAPACK's dgesv and dgesvx require the matrix to be square and invertible. The present class does the same. It will assert that the matrix is square, but it won't (actually it can't) check that the matrix is invertible: it is your task to check that you only use this decomposition on invertible matrices.</p>
<p>The guaranteed safe alternative, working for all matrices, is the full pivoting LU decomposition, provided by class <a class="el" href="classEigen_1_1FullPivLU.html" title="LU decomposition of a matrix with complete pivoting, and related features.">FullPivLU</a>.</p>
<p>This is <b>not</b> a rank-revealing LU decomposition. Many features are intentionally absent from this class, such as rank computation. If you need these features, use class <a class="el" href="classEigen_1_1FullPivLU.html" title="LU decomposition of a matrix with complete pivoting, and related features.">FullPivLU</a>.</p>
<p>This LU decomposition is suitable to invert invertible matrices. It is what <a class="el" href="classEigen_1_1MatrixBase.html#a7712eb69e8ea3c8f7b8da1c44dbdeebf">MatrixBase::inverse()</a> uses in the general case. On the other hand, it is <b>not</b> suitable to determine whether a given matrix is invertible.</p>
<p>The data of the LU decomposition can be directly accessed through the methods <a class="el" href="classEigen_1_1PartialPivLU.html#af7a4a4cddfb87ea31ac03c83712bdc51">matrixLU()</a>, <a class="el" href="classEigen_1_1PartialPivLU.html#a8750517c27cde70868cae99cda085239">permutationP()</a>.</p>
<p>This class supports the <a class="el" href="group__InplaceDecomposition.html">inplace decomposition </a> mechanism.</p>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1MatrixBase.html#a6199d8aaf26c1b8ac3097fdfa7733a1e">MatrixBase::partialPivLu()</a>, <a class="el" href="classEigen_1_1MatrixBase.html#a7ad8f77004bb956b603bb43fd2e3c061">MatrixBase::determinant()</a>, <a class="el" href="classEigen_1_1MatrixBase.html#a7712eb69e8ea3c8f7b8da1c44dbdeebf">MatrixBase::inverse()</a>, MatrixBase::computeInverse(), class <a class="el" href="classEigen_1_1FullPivLU.html" title="LU decomposition of a matrix with complete pivoting, and related features.">FullPivLU</a> </dd></dl>
</div><div id="dynsection-0" onclick="return toggleVisibility(this)" class="dynheader closed" style="cursor:pointer;">
  <img id="dynsection-0-trigger" src="closed.png" alt="+"/> Inheritance diagram for Eigen::PartialPivLU&lt; MatrixType_ &gt;:</div>
<div id="dynsection-0-summary" class="dynsummary" style="display:block;">
</div>
<div id="dynsection-0-content" class="dyncontent" style="display:none;">
<div class="center"><img src="classEigen_1_1PartialPivLU__inherit__graph.png" border="0" usemap="#aEigen_1_1PartialPivLU_3_01MatrixType___01_4_inherit__map" alt="Inheritance graph"/></div>
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<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:a54c3d39c9b46ff485a8d2140b9b23193"><td class="memItemLeft" align="right" valign="top">Scalar&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1PartialPivLU.html#a54c3d39c9b46ff485a8d2140b9b23193">determinant</a> () const</td></tr>
<tr class="separator:a54c3d39c9b46ff485a8d2140b9b23193"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9eab2171cf4d0018fdce54ee8b5e6cf0"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Inverse.html">Inverse</a>&lt; <a class="el" href="classEigen_1_1PartialPivLU.html">PartialPivLU</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1PartialPivLU.html#a9eab2171cf4d0018fdce54ee8b5e6cf0">inverse</a> () const</td></tr>
<tr class="separator:a9eab2171cf4d0018fdce54ee8b5e6cf0"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:af7a4a4cddfb87ea31ac03c83712bdc51"><td class="memItemLeft" align="right" valign="top">const MatrixType &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1PartialPivLU.html#af7a4a4cddfb87ea31ac03c83712bdc51">matrixLU</a> () const</td></tr>
<tr class="separator:af7a4a4cddfb87ea31ac03c83712bdc51"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a5c04818d354f94a98786d8a44cb709c6"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1PartialPivLU.html#a5c04818d354f94a98786d8a44cb709c6">PartialPivLU</a> ()</td></tr>
<tr class="memdesc:a5c04818d354f94a98786d8a44cb709c6"><td class="mdescLeft">&#160;</td><td class="mdescRight">Default Constructor.  <a href="classEigen_1_1PartialPivLU.html#a5c04818d354f94a98786d8a44cb709c6">More...</a><br /></td></tr>
<tr class="separator:a5c04818d354f94a98786d8a44cb709c6"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:acf37214aebb54d0e186ae39ac6c41bdf"><td class="memTemplParams" colspan="2">template&lt;typename InputType &gt; </td></tr>
<tr class="memitem:acf37214aebb54d0e186ae39ac6c41bdf"><td class="memTemplItemLeft" align="right" valign="top">&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1PartialPivLU.html#acf37214aebb54d0e186ae39ac6c41bdf">PartialPivLU</a> (const <a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;matrix)</td></tr>
<tr class="separator:acf37214aebb54d0e186ae39ac6c41bdf"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a4efc917d31d0e9d76781a97509309061"><td class="memTemplParams" colspan="2">template&lt;typename InputType &gt; </td></tr>
<tr class="memitem:a4efc917d31d0e9d76781a97509309061"><td class="memTemplItemLeft" align="right" valign="top">&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1PartialPivLU.html#a4efc917d31d0e9d76781a97509309061">PartialPivLU</a> (<a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;matrix)</td></tr>
<tr class="separator:a4efc917d31d0e9d76781a97509309061"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:acf892c12d8a229b32bddc3149e32e63a"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1PartialPivLU.html#acf892c12d8a229b32bddc3149e32e63a">PartialPivLU</a> (<a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> <a class="el" href="structEigen_1_1EigenBase.html#ae106171b6fefd3f7af108a8283de36c9">size</a>)</td></tr>
<tr class="memdesc:acf892c12d8a229b32bddc3149e32e63a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Default Constructor with memory preallocation.  <a href="classEigen_1_1PartialPivLU.html#acf892c12d8a229b32bddc3149e32e63a">More...</a><br /></td></tr>
<tr class="separator:acf892c12d8a229b32bddc3149e32e63a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a8750517c27cde70868cae99cda085239"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1PermutationMatrix.html">PermutationType</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1PartialPivLU.html#a8750517c27cde70868cae99cda085239">permutationP</a> () const</td></tr>
<tr class="separator:a8750517c27cde70868cae99cda085239"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a05da6009014b7eae4b3eed952884d49b"><td class="memItemLeft" align="right" valign="top">RealScalar&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1PartialPivLU.html#a05da6009014b7eae4b3eed952884d49b">rcond</a> () const</td></tr>
<tr class="separator:a05da6009014b7eae4b3eed952884d49b"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aba7f1ee83537b0d240ebf206503a4920"><td class="memItemLeft" align="right" valign="top">MatrixType&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1PartialPivLU.html#aba7f1ee83537b0d240ebf206503a4920">reconstructedMatrix</a> () const</td></tr>
<tr class="separator:aba7f1ee83537b0d240ebf206503a4920"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a03baa6cff14f16982230d4fd7e0e8118"><td class="memTemplParams" colspan="2">template&lt;typename Rhs &gt; </td></tr>
<tr class="memitem:a03baa6cff14f16982230d4fd7e0e8118"><td class="memTemplItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Solve.html">Solve</a>&lt; <a class="el" href="classEigen_1_1PartialPivLU.html">PartialPivLU</a>, Rhs &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1PartialPivLU.html#a03baa6cff14f16982230d4fd7e0e8118">solve</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>&lt; Rhs &gt; &amp;b) const</td></tr>
<tr class="separator:a03baa6cff14f16982230d4fd7e0e8118"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="inherit_header pub_methods_classEigen_1_1SolverBase"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_classEigen_1_1SolverBase')"><img src="closed.png" alt="-"/>&#160;Public Member Functions inherited from <a class="el" href="classEigen_1_1SolverBase.html">Eigen::SolverBase&lt; PartialPivLU&lt; MatrixType_ &gt; &gt;</a></td></tr>
<tr class="memitem:ae1025416bdb5a768f7213c67feb4dc33 inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const AdjointReturnType&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#ae1025416bdb5a768f7213c67feb4dc33">adjoint</a> () const</td></tr>
<tr class="separator:ae1025416bdb5a768f7213c67feb4dc33 inherit pub_methods_classEigen_1_1SolverBase"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1fbabe7f12bcbfba3b9a448b1f5e46fa inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1PartialPivLU.html">PartialPivLU</a>&lt; MatrixType_ &gt; &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a> ()</td></tr>
<tr class="separator:a1fbabe7f12bcbfba3b9a448b1f5e46fa inherit pub_methods_classEigen_1_1SolverBase"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:afd4f3f1c57b7594b96a7e30f2974ea2e inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1PartialPivLU.html">PartialPivLU</a>&lt; MatrixType_ &gt; &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#afd4f3f1c57b7594b96a7e30f2974ea2e">derived</a> () const</td></tr>
<tr class="separator:afd4f3f1c57b7594b96a7e30f2974ea2e inherit pub_methods_classEigen_1_1SolverBase"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a7fd647d110487799205df6f99547879d inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Solve.html">Solve</a>&lt; <a class="el" href="classEigen_1_1PartialPivLU.html">PartialPivLU</a>&lt; MatrixType_ &gt;, Rhs &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a7fd647d110487799205df6f99547879d">solve</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>&lt; Rhs &gt; &amp;b) const</td></tr>
<tr class="separator:a7fd647d110487799205df6f99547879d inherit pub_methods_classEigen_1_1SolverBase"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a4d5e5baddfba3790ab1a5f247dcc4dc1 inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a4d5e5baddfba3790ab1a5f247dcc4dc1">SolverBase</a> ()</td></tr>
<tr class="separator:a4d5e5baddfba3790ab1a5f247dcc4dc1 inherit pub_methods_classEigen_1_1SolverBase"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a70cf5cd1b31dbb4f4d61c436c83df6d3 inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Transpose.html">ConstTransposeReturnType</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a70cf5cd1b31dbb4f4d61c436c83df6d3">transpose</a> () const</td></tr>
<tr class="separator:a70cf5cd1b31dbb4f4d61c436c83df6d3 inherit pub_methods_classEigen_1_1SolverBase"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="inherit_header pub_methods_structEigen_1_1EigenBase"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_structEigen_1_1EigenBase')"><img src="closed.png" alt="-"/>&#160;Public Member Functions inherited from <a class="el" href="structEigen_1_1EigenBase.html">Eigen::EigenBase&lt; Derived &gt;</a></td></tr>
<tr class="memitem:a2d768a9877f5f69f49432d447b552bfe inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">EIGEN_CONSTEXPR <a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#a2d768a9877f5f69f49432d447b552bfe">cols</a> () const EIGEN_NOEXCEPT</td></tr>
<tr class="separator:a2d768a9877f5f69f49432d447b552bfe inherit pub_methods_structEigen_1_1EigenBase"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1fbabe7f12bcbfba3b9a448b1f5e46fa inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">Derived &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a> ()</td></tr>
<tr class="separator:a1fbabe7f12bcbfba3b9a448b1f5e46fa inherit pub_methods_structEigen_1_1EigenBase"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:afd4f3f1c57b7594b96a7e30f2974ea2e inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">const Derived &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#afd4f3f1c57b7594b96a7e30f2974ea2e">derived</a> () const</td></tr>
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<tr class="memitem:ac22eb0695d00edd7d4a3b2d0a98b81c2 inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">EIGEN_CONSTEXPR <a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a> () const EIGEN_NOEXCEPT</td></tr>
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<tr class="memitem:ae106171b6fefd3f7af108a8283de36c9 inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">EIGEN_CONSTEXPR <a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#ae106171b6fefd3f7af108a8283de36c9">size</a> () const EIGEN_NOEXCEPT</td></tr>
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Additional Inherited Members</h2></td></tr>
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<tr class="memitem:a554f30542cc2316add4b1ea0a492ff02 inherit pub_types_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a></td></tr>
<tr class="memdesc:a554f30542cc2316add4b1ea0a492ff02 inherit pub_types_structEigen_1_1EigenBase"><td class="mdescLeft">&#160;</td><td class="mdescRight">The interface type of indices.  <a href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">More...</a><br /></td></tr>
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<h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a5c04818d354f94a98786d8a44cb709c6">&#9670;&nbsp;</a></span>PartialPivLU() <span class="overload">[1/4]</span></h2>

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<p>Default Constructor. </p>
<p>The default constructor is useful in cases in which the user intends to perform decompositions via PartialPivLU::compute(const MatrixType&amp;). </p>

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<h2 class="memtitle"><span class="permalink"><a href="#acf892c12d8a229b32bddc3149e32e63a">&#9670;&nbsp;</a></span>PartialPivLU() <span class="overload">[2/4]</span></h2>

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          <td>(</td>
          <td class="paramtype"><a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td>
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<p>Default Constructor with memory preallocation. </p>
<p>Like the default constructor but with preallocation of the internal data according to the specified problem <em>size</em>. </p><dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1PartialPivLU.html#a5c04818d354f94a98786d8a44cb709c6" title="Default Constructor.">PartialPivLU()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#acf37214aebb54d0e186ae39ac6c41bdf">&#9670;&nbsp;</a></span>PartialPivLU() <span class="overload">[3/4]</span></h2>

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          <td>(</td>
          <td class="paramtype">const <a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;&#160;</td>
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<p>Constructor.</p>
<dl class="params"><dt>Parameters</dt><dd>
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<dl class="section warning"><dt>Warning</dt><dd>The matrix should have full rank (e.g. if it's square, it should be invertible). If you need to deal with non-full rank, use class <a class="el" href="classEigen_1_1FullPivLU.html" title="LU decomposition of a matrix with complete pivoting, and related features.">FullPivLU</a> instead. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a4efc917d31d0e9d76781a97509309061">&#9670;&nbsp;</a></span>PartialPivLU() <span class="overload">[4/4]</span></h2>

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          <td>(</td>
          <td class="paramtype"><a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;&#160;</td>
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<p>Constructor for <a class="el" href="group__InplaceDecomposition.html">inplace decomposition </a></p>
<dl class="params"><dt>Parameters</dt><dd>
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    <tr><td class="paramname">matrix</td><td>the matrix of which to compute the LU decomposition.</td></tr>
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<dl class="section warning"><dt>Warning</dt><dd>The matrix should have full rank (e.g. if it's square, it should be invertible). If you need to deal with non-full rank, use class <a class="el" href="classEigen_1_1FullPivLU.html" title="LU decomposition of a matrix with complete pivoting, and related features.">FullPivLU</a> instead. </dd></dl>

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<h2 class="groupheader">Member Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a54c3d39c9b46ff485a8d2140b9b23193">&#9670;&nbsp;</a></span>determinant()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the determinant of the matrix of which *this is the LU decomposition. It has only linear complexity (that is, O(n) where n is the dimension of the square matrix) as the LU decomposition has already been computed.</dd></dl>
<dl class="section note"><dt>Note</dt><dd>For fixed-size matrices of size up to 4, <a class="el" href="classEigen_1_1MatrixBase.html#a7ad8f77004bb956b603bb43fd2e3c061">MatrixBase::determinant()</a> offers optimized paths.</dd></dl>
<dl class="section warning"><dt>Warning</dt><dd>a determinant can be very big or small, so for matrices of large enough dimension, there is a risk of overflow/underflow.</dd></dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1MatrixBase.html#a7ad8f77004bb956b603bb43fd2e3c061">MatrixBase::determinant()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a9eab2171cf4d0018fdce54ee8b5e6cf0">&#9670;&nbsp;</a></span>inverse()</h2>

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          <td class="memname">const <a class="el" href="classEigen_1_1Inverse.html">Inverse</a>&lt;<a class="el" href="classEigen_1_1PartialPivLU.html">PartialPivLU</a>&gt; <a class="el" href="classEigen_1_1PartialPivLU.html">Eigen::PartialPivLU</a>&lt; MatrixType_ &gt;::inverse </td>
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<dl class="section return"><dt>Returns</dt><dd>the inverse of the matrix of which *this is the LU decomposition.</dd></dl>
<dl class="section warning"><dt>Warning</dt><dd>The matrix being decomposed here is assumed to be invertible. If you need to check for invertibility, use class <a class="el" href="classEigen_1_1FullPivLU.html" title="LU decomposition of a matrix with complete pivoting, and related features.">FullPivLU</a> instead.</dd></dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1MatrixBase.html#a7712eb69e8ea3c8f7b8da1c44dbdeebf">MatrixBase::inverse()</a>, LU::inverse() </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#af7a4a4cddfb87ea31ac03c83712bdc51">&#9670;&nbsp;</a></span>matrixLU()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the LU decomposition matrix: the upper-triangular part is U, the unit-lower-triangular part is L (at least for square matrices; in the non-square case, special care is needed, see the documentation of class <a class="el" href="classEigen_1_1FullPivLU.html" title="LU decomposition of a matrix with complete pivoting, and related features.">FullPivLU</a>).</dd></dl>
<dl class="section see"><dt>See also</dt><dd>matrixL(), matrixU() </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a8750517c27cde70868cae99cda085239">&#9670;&nbsp;</a></span>permutationP()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the permutation matrix P. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a05da6009014b7eae4b3eed952884d49b">&#9670;&nbsp;</a></span>rcond()</h2>

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<dl class="section return"><dt>Returns</dt><dd>an estimate of the reciprocal condition number of the matrix of which <code>*this</code> is the LU decomposition. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#aba7f1ee83537b0d240ebf206503a4920">&#9670;&nbsp;</a></span>reconstructedMatrix()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the matrix represented by the decomposition, i.e., it returns the product: P^{-1} L U. This function is provided for debug purpose. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a03baa6cff14f16982230d4fd7e0e8118">&#9670;&nbsp;</a></span>solve()</h2>

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          <td>(</td>
          <td class="paramtype">const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>&lt; Rhs &gt; &amp;&#160;</td>
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<p>This method returns the solution x to the equation Ax=b, where A is the matrix of which *this is the LU decomposition.</p>
<dl class="params"><dt>Parameters</dt><dd>
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    <tr><td class="paramname">b</td><td>the right-hand-side of the equation to solve. Can be a vector or a matrix, the only requirement in order for the equation to make sense is that b.rows()==A.rows(), where A is the matrix of which *this is the LU decomposition.</td></tr>
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<dl class="section return"><dt>Returns</dt><dd>the solution.</dd></dl>
<p>Example: </p><div class="fragment"><div class="line"><a class="code" href="group__matrixtypedefs.html#ga99b41a69f0bf64eadb63a97f357ab412">MatrixXd</a> A = <a class="code" href="classEigen_1_1DenseBase.html#ae814abb451b48ed872819192dc188c19">MatrixXd::Random</a>(3,3);</div>
<div class="line"><a class="code" href="group__matrixtypedefs.html#ga99b41a69f0bf64eadb63a97f357ab412">MatrixXd</a> B = <a class="code" href="classEigen_1_1DenseBase.html#ae814abb451b48ed872819192dc188c19">MatrixXd::Random</a>(3,2);</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;Here is the invertible matrix A:&quot;</span> &lt;&lt; endl &lt;&lt; A &lt;&lt; endl;</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;Here is the matrix B:&quot;</span> &lt;&lt; endl &lt;&lt; B &lt;&lt; endl;</div>
<div class="line"><a class="code" href="group__matrixtypedefs.html#ga99b41a69f0bf64eadb63a97f357ab412">MatrixXd</a> X = A.lu().solve(B);</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;Here is the (unique) solution X to the equation AX=B:&quot;</span> &lt;&lt; endl &lt;&lt; X &lt;&lt; endl;</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;Relative error: &quot;</span> &lt;&lt; (A*X-B).norm() / B.norm() &lt;&lt; endl;</div>
<div class="ttc" id="aclassEigen_1_1DenseBase_html_ae814abb451b48ed872819192dc188c19"><div class="ttname"><a href="classEigen_1_1DenseBase.html#ae814abb451b48ed872819192dc188c19">Eigen::DenseBase::Random</a></div><div class="ttdeci">static const RandomReturnType Random()</div><div class="ttdef"><b>Definition:</b> Random.h:114</div></div>
<div class="ttc" id="agroup__matrixtypedefs_html_ga99b41a69f0bf64eadb63a97f357ab412"><div class="ttname"><a href="group__matrixtypedefs.html#ga99b41a69f0bf64eadb63a97f357ab412">Eigen::MatrixXd</a></div><div class="ttdeci">Matrix&lt; double, Dynamic, Dynamic &gt; MatrixXd</div><div class="ttdoc">Dynamic×Dynamic matrix of type double.</div><div class="ttdef"><b>Definition:</b> Matrix.h:501</div></div>
</div><!-- fragment --><p> Output: </p><pre class="fragment">Here is the invertible matrix A:
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
Here is the matrix B:
  0.108   -0.27
-0.0452  0.0268
  0.258   0.904
Here is the (unique) solution X to the equation AX=B:
 0.609   2.68
-0.231  -1.57
  0.51   3.51
Relative error: 3.28e-16
</pre><p>Since this <a class="el" href="classEigen_1_1PartialPivLU.html" title="LU decomposition of a matrix with partial pivoting, and related features.">PartialPivLU</a> class assumes anyway that the matrix A is invertible, the solution theoretically exists and is unique regardless of b.</p>
<dl class="section see"><dt>See also</dt><dd>TriangularView::solve(), <a class="el" href="classEigen_1_1PartialPivLU.html#a9eab2171cf4d0018fdce54ee8b5e6cf0">inverse()</a>, computeInverse() </dd></dl>

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<hr/>The documentation for this class was generated from the following file:<ul>
<li><a class="el" href="PartialPivLU_8h_source.html">PartialPivLU.h</a></li>
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